Optical interferometry has been a basic technique of distance metrology for many years. Typically, an optical interferometer having a sensitive optical path including the entire distance to be measured is employed. Variations of this distance on the order of half an optical wavelength will cause the interferometer output to change from constructive interference to destructive interference, or vice versa. Such an interferometer fringe can easily be detected. With advanced measurement techniques, a small fraction of an interferometer fringe can be detected, thereby providing measurement precision on the order of a small fraction of the optical wavelength.
However, this general approach for distance measurement encounters severe difficulties in applications having extremely demanding performance requirements, such as space-based optical interferometry for gravitational wave detection. To appreciate these difficulties, it is helpful to consider a brief description of such a system. A space based interferometer includes several spacecraft, each spacecraft including at least one gravitational proof mass. Detection of gravitational waves is based on detecting corresponding changes in proof mass position. Ideally, the only forces acting on the proof masses are gravitational forces, and a key aspect of the system design is to approach this ideal as closely as possible.
Since the expected effect of gravitational waves on proof mass position is exceedingly small (e.g., the Laser Interferometer Space Antenna (LISA) requires a measurement precision of ˜10 pm Hz−1/2 from 0.1 mHz to 1 Hz, and the Big Bang Observatory requires a measurement precision of ˜1 fm Hz−1/2 from 0.1 to 10 Hz), extreme measures are taken to protect the proof mass from external forces. For example, an enclosure around the proof mass can be employed to shield the proof mass from the external force due to the solar wind (or other ambient perturbations). In such situations, the spacecraft is controlled to maintain a certain separation between the enclosure and proof mass, so that the spacecraft is referenced relative to the proof mass (as opposed to the other way around).
In this context, the traditional optical interferometry approach of including the entire distance between the proof masses in a sensitive interferometer path encounters severe difficulties. In particular, such an approach entails passing interferometer light through a window in the enclosure to reach the proof mass. This window is a transmissive optical element in the sensitive interferometer path. Thus, optical path length changes of the window due to the temperature dependence of the refractive index (i.e., dn/dT) are a significant source of measurement error. Thermal expansion of the window is also a relevant source of error, but tends to be less significant than the dn/dT effect. Detailed system analysis including realistic limits on achievable temperature control shows that having transmissive optical elements in a high-precision interferometer is highly undesirable, and can degrade system-level performance.
Another difficulty is that the radiation pressure of the external interferometer light on the proof mass is an undesirable net external force on the proof mass.
Accordingly, it would be an advance in the art to provide interferometric distance measurement that does not require transmissive optical elements in the interferometer to measure the distance to an enclosed object.